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הגדרות
תרומה לוויקיספר
אודות ויקיספר
הבהרות משפטיות
חיפוש
מתמטיקה תיכונית/אלגברה תיכונית/משוואות/משוואות פשוטות בנעלם אחד/תרגילים/רמה ד
שפה
מעקב
עריכה
<
מתמטיקה תיכונית
|
אלגברה תיכונית
|
משוואות
|
משוואות פשוטות בנעלם אחד
|
תרגילים
תרגילים
עריכה
פתרו את המשוואות הבאות (מותר להשתמש במחשבון – המספרים גדולים):
−
4
3
x
−
2
13
x
−
11
6
x
−
1
6
x
−
6
11
x
=
10
9
x
+
13
x
−
3
10
+
1
4
−
933897
2860
{\displaystyle -{\frac {4}{3}}x-{\frac {2}{13}}x-{\frac {11}{6}}x-{\frac {1}{6}}x-{\frac {6}{11}}x={\frac {10}{9}}x+13x-{\frac {3}{10}}+{\frac {1}{4}}-{\frac {933897}{2860}}}
−
3
5
x
−
7
9
x
−
7
2
−
11
12
x
−
2
7
+
5
7
x
=
−
13
7
x
−
13
10
x
+
7
3
x
−
2543
420
{\displaystyle -{\frac {3}{5}}x-{\frac {7}{9}}x-{\frac {7}{2}}-{\frac {11}{12}}x-{\frac {2}{7}}+{\frac {5}{7}}x=-{\frac {13}{7}}x-{\frac {13}{10}}x+{\frac {7}{3}}x-{\frac {2543}{420}}}
−
3
2
x
−
8
13
x
−
8
x
+
2
7
=
−
1
−
10
9
+
5
14
x
+
7
4
x
−
1
10
+
1221679
8190
{\displaystyle -{\frac {3}{2}}x-{\frac {8}{13}}x-8x+{\frac {2}{7}}=-1-{\frac {10}{9}}+{\frac {5}{14}}x+{\frac {7}{4}}x-{\frac {1}{10}}+{\frac {1221679}{8190}}}
−
11
9
−
5
9
x
+
7
3
x
+
5
9
x
−
3
5
x
−
9
10
=
−
1
6
+
6
7
+
3
13
x
+
43859
4095
{\displaystyle -{\frac {11}{9}}-{\frac {5}{9}}x+{\frac {7}{3}}x+{\frac {5}{9}}x-{\frac {3}{5}}x-{\frac {9}{10}}=-{\frac {1}{6}}+{\frac {6}{7}}+{\frac {3}{13}}x+{\frac {43859}{4095}}}
3
2
−
14
11
−
5
7
x
+
13
8
=
7
−
3
5
+
3
10
x
+
5
2
+
1
2
+
2927
440
{\displaystyle {\frac {3}{2}}-{\frac {14}{11}}-{\frac {5}{7}}x+{\frac {13}{8}}=7-{\frac {3}{5}}+{\frac {3}{10}}x+{\frac {5}{2}}+{\frac {1}{2}}+{\frac {2927}{440}}}
3
5
+
2
−
8
7
x
=
−
4
3
x
+
1
8
x
+
x
+
13
x
+
9
11
x
+
1
3
−
388001
9240
{\displaystyle {\frac {3}{5}}+2-{\frac {8}{7}}x=-{\frac {4}{3}}x+{\frac {1}{8}}x+x+13x+{\frac {9}{11}}x+{\frac {1}{3}}-{\frac {388001}{9240}}}
−
1
2
x
+
6
5
+
5
12
x
−
2
+
4
3
+
3
11
x
=
−
2
3
x
+
1
6
+
7
3
−
4123
660
{\displaystyle -{\frac {1}{2}}x+{\frac {6}{5}}+{\frac {5}{12}}x-2+{\frac {4}{3}}+{\frac {3}{11}}x=-{\frac {2}{3}}x+{\frac {1}{6}}+{\frac {7}{3}}-{\frac {4123}{660}}}
1
12
+
7
12
x
−
2
3
x
−
13
8
−
13
3
x
=
6
5
x
+
12
5
x
+
4
−
7
2
+
913
24
{\displaystyle {\frac {1}{12}}+{\frac {7}{12}}x-{\frac {2}{3}}x-{\frac {13}{8}}-{\frac {13}{3}}x={\frac {6}{5}}x+{\frac {12}{5}}x+4-{\frac {7}{2}}+{\frac {913}{24}}}
3
2
−
6
x
−
5
6
−
3
5
−
1
2
x
+
7
8
=
10
9
+
5
7
x
+
9
10
x
+
265397
2520
{\displaystyle {\frac {3}{2}}-6x-{\frac {5}{6}}-{\frac {3}{5}}-{\frac {1}{2}}x+{\frac {7}{8}}={\frac {10}{9}}+{\frac {5}{7}}x+{\frac {9}{10}}x+{\frac {265397}{2520}}}
11
6
x
+
3
4
x
+
1
2
−
14
11
x
+
11
4
=
−
13
3
+
2
−
7
x
−
x
+
5899
66
{\displaystyle {\frac {11}{6}}x+{\frac {3}{4}}x+{\frac {1}{2}}-{\frac {14}{11}}x+{\frac {11}{4}}=-{\frac {13}{3}}+2-7x-x+{\frac {5899}{66}}}
1
7
x
+
1
9
x
−
12
7
+
2
+
1
2
=
−
5
9
x
+
11
5
x
−
14
11
x
+
13
4
x
+
110123
1540
{\displaystyle {\frac {1}{7}}x+{\frac {1}{9}}x-{\frac {12}{7}}+2+{\frac {1}{2}}=-{\frac {5}{9}}x+{\frac {11}{5}}x-{\frac {14}{11}}x+{\frac {13}{4}}x+{\frac {110123}{1540}}}
1
10
x
−
7
10
+
7
5
x
+
5
x
−
6
11
=
−
5
9
x
−
3
4
x
−
14
5
x
+
3
2
x
+
8946
55
{\displaystyle {\frac {1}{10}}x-{\frac {7}{10}}+{\frac {7}{5}}x+5x-{\frac {6}{11}}=-{\frac {5}{9}}x-{\frac {3}{4}}x-{\frac {14}{5}}x+{\frac {3}{2}}x+{\frac {8946}{55}}}
13
5
x
+
13
x
+
13
14
x
+
6
=
−
1
10
+
10
13
+
9
13
+
1
3
−
1
2
−
83687
1365
{\displaystyle {\frac {13}{5}}x+13x+{\frac {13}{14}}x+6=-{\frac {1}{10}}+{\frac {10}{13}}+{\frac {9}{13}}+{\frac {1}{3}}-{\frac {1}{2}}-{\frac {83687}{1365}}}
7
4
+
1
+
9
8
x
−
1
5
+
13
12
x
−
11
x
=
2
3
−
13
11
−
4
x
−
116129
1320
{\displaystyle {\frac {7}{4}}+1+{\frac {9}{8}}x-{\frac {1}{5}}+{\frac {13}{12}}x-11x={\frac {2}{3}}-{\frac {13}{11}}-4x-{\frac {116129}{1320}}}
7
11
x
−
5
13
+
5
4
−
1
−
x
=
2
−
1
2
x
+
4
x
−
11
−
28079
572
{\displaystyle {\frac {7}{11}}x-{\frac {5}{13}}+{\frac {5}{4}}-1-x=2-{\frac {1}{2}}x+4x-11-{\frac {28079}{572}}}
−
13
7
−
1
7
x
+
3
13
x
−
5
7
−
3
4
x
−
x
=
6
5
−
1
2
+
9
2
x
+
4119
455
{\displaystyle -{\frac {13}{7}}-{\frac {1}{7}}x+{\frac {3}{13}}x-{\frac {5}{7}}-{\frac {3}{4}}x-x={\frac {6}{5}}-{\frac {1}{2}}+{\frac {9}{2}}x+{\frac {4119}{455}}}
7
8
−
13
9
x
−
2
9
−
2
5
x
+
x
=
13
9
+
3
−
10
13
−
1
4
x
+
11977
1560
{\displaystyle {\frac {7}{8}}-{\frac {13}{9}}x-{\frac {2}{9}}-{\frac {2}{5}}x+x={\frac {13}{9}}+3-{\frac {10}{13}}-{\frac {1}{4}}x+{\frac {11977}{1560}}}
−
3
−
13
11
−
12
13
x
+
1
2
x
+
11
10
−
4
9
x
−
1
14
x
=
2
11
+
1
7
+
60983
6930
{\displaystyle -3-{\frac {13}{11}}-{\frac {12}{13}}x+{\frac {1}{2}}x+{\frac {11}{10}}-{\frac {4}{9}}x-{\frac {1}{14}}x={\frac {2}{11}}+{\frac {1}{7}}+{\frac {60983}{6930}}}
−
x
+
9
10
x
−
13
+
1
9
−
5
13
x
−
13
4
=
7
8
+
1
+
8
11
−
939847
51480
{\displaystyle -x+{\frac {9}{10}}x-13+{\frac {1}{9}}-{\frac {5}{13}}x-{\frac {13}{4}}={\frac {7}{8}}+1+{\frac {8}{11}}-{\frac {939847}{51480}}}
−
2
9
+
x
+
10
7
+
4
3
x
−
1
+
12
11
+
11
7
=
−
10
13
+
2
3
+
51872
1287
{\displaystyle -{\frac {2}{9}}+x+{\frac {10}{7}}+{\frac {4}{3}}x-1+{\frac {12}{11}}+{\frac {11}{7}}=-{\frac {10}{13}}+{\frac {2}{3}}+{\frac {51872}{1287}}}
−
2
5
−
5
2
−
7
x
+
13
10
x
+
12
11
−
3
=
−
13
5
x
−
1
11
x
−
7
13
+
2499
1430
{\displaystyle -{\frac {2}{5}}-{\frac {5}{2}}-7x+{\frac {13}{10}}x+{\frac {12}{11}}-3=-{\frac {13}{5}}x-{\frac {1}{11}}x-{\frac {7}{13}}+{\frac {2499}{1430}}}
1
3
+
4
3
x
+
7
6
x
+
1
+
9
8
+
2
13
x
+
3
=
7
3
+
1
6
+
17483
312
{\displaystyle {\frac {1}{3}}+{\frac {4}{3}}x+{\frac {7}{6}}x+1+{\frac {9}{8}}+{\frac {2}{13}}x+3={\frac {7}{3}}+{\frac {1}{6}}+{\frac {17483}{312}}}
−
1
11
x
+
13
8
x
+
6
5
x
−
13
14
x
−
1
=
2
x
+
7
6
+
4
3
+
4
7
x
+
1493
440
{\displaystyle -{\frac {1}{11}}x+{\frac {13}{8}}x+{\frac {6}{5}}x-{\frac {13}{14}}x-1=2x+{\frac {7}{6}}+{\frac {4}{3}}+{\frac {4}{7}}x+{\frac {1493}{440}}}
−
3
10
x
−
6
7
+
9
2
x
+
5
8
x
=
−
5
7
x
−
7
4
−
3
11
−
11
13
x
+
6
5
x
+
383059
8008
{\displaystyle -{\frac {3}{10}}x-{\frac {6}{7}}+{\frac {9}{2}}x+{\frac {5}{8}}x=-{\frac {5}{7}}x-{\frac {7}{4}}-{\frac {3}{11}}-{\frac {11}{13}}x+{\frac {6}{5}}x+{\frac {383059}{8008}}}
11
10
+
3
5
x
−
7
3
x
+
3
8
x
=
1
12
+
7
4
x
−
8
3
x
−
14
13
x
−
13
5
−
38
195
{\displaystyle {\frac {11}{10}}+{\frac {3}{5}}x-{\frac {7}{3}}x+{\frac {3}{8}}x={\frac {1}{12}}+{\frac {7}{4}}x-{\frac {8}{3}}x-{\frac {14}{13}}x-{\frac {13}{5}}-{\frac {38}{195}}}
−
3
x
−
3
2
+
4
+
5
7
x
+
5
+
13
2
x
+
4
x
=
4
3
−
3
10
x
+
7411
42
{\displaystyle -3x-{\frac {3}{2}}+4+{\frac {5}{7}}x+5+{\frac {13}{2}}x+4x={\frac {4}{3}}-{\frac {3}{10}}x+{\frac {7411}{42}}}
2
7
x
−
7
2
x
−
13
6
+
13
x
+
1
8
x
=
9
10
+
1
4
−
8
9
−
1
11
−
703007
6930
{\displaystyle {\frac {2}{7}}x-{\frac {7}{2}}x-{\frac {13}{6}}+13x+{\frac {1}{8}}x={\frac {9}{10}}+{\frac {1}{4}}-{\frac {8}{9}}-{\frac {1}{11}}-{\frac {703007}{6930}}}
−
5
2
−
2
x
−
10
7
x
+
13
6
+
5
2
x
=
4
13
x
+
1
8
+
1
3
x
−
5
3
x
−
365
2184
{\displaystyle -{\frac {5}{2}}-2x-{\frac {10}{7}}x+{\frac {13}{6}}+{\frac {5}{2}}x={\frac {4}{13}}x+{\frac {1}{8}}+{\frac {1}{3}}x-{\frac {5}{3}}x-{\frac {365}{2184}}}
−
1
2
−
9
8
+
5
4
x
+
x
+
3
=
−
2
+
x
+
11
7
x
+
9
8
+
99
28
{\displaystyle -{\frac {1}{2}}-{\frac {9}{8}}+{\frac {5}{4}}x+x+3=-2+x+{\frac {11}{7}}x+{\frac {9}{8}}+{\frac {99}{28}}}
−
11
x
+
13
x
+
2
9
x
+
2
3
+
7
=
1
9
+
14
5
x
+
4
13
−
5
6
+
1891
234
{\displaystyle -11x+13x+{\frac {2}{9}}x+{\frac {2}{3}}+7={\frac {1}{9}}+{\frac {14}{5}}x+{\frac {4}{13}}-{\frac {5}{6}}+{\frac {1891}{234}}}
7
6
x
+
13
8
x
+
13
14
+
2
x
=
−
5
x
+
2
11
+
4
x
−
9
2
+
9
x
−
5121
154
{\displaystyle {\frac {7}{6}}x+{\frac {13}{8}}x+{\frac {13}{14}}+2x=-5x+{\frac {2}{11}}+4x-{\frac {9}{2}}+9x-{\frac {5121}{154}}}
−
x
−
1
7
−
7
x
+
13
4
+
10
7
x
−
3
=
13
10
−
1
4
x
−
1
4
x
−
2717
140
{\displaystyle -x-{\frac {1}{7}}-7x+{\frac {13}{4}}+{\frac {10}{7}}x-3={\frac {13}{10}}-{\frac {1}{4}}x-{\frac {1}{4}}x-{\frac {2717}{140}}}
7
3
−
4
3
−
4
5
x
+
11
4
x
−
2
x
=
5
x
+
x
+
14
3
x
−
1
+
2602
15
{\displaystyle {\frac {7}{3}}-{\frac {4}{3}}-{\frac {4}{5}}x+{\frac {11}{4}}x-2x=5x+x+{\frac {14}{3}}x-1+{\frac {2602}{15}}}
7
4
x
+
1
3
+
9
14
−
1
+
1
−
7
9
x
−
2
x
=
−
3
11
+
2
+
10355
1386
{\displaystyle {\frac {7}{4}}x+{\frac {1}{3}}+{\frac {9}{14}}-1+1-{\frac {7}{9}}x-2x=-{\frac {3}{11}}+2+{\frac {10355}{1386}}}
3
4
−
2
5
x
+
9
4
x
+
5
14
x
=
−
1
2
+
6
7
x
−
10
9
x
−
1
+
1
7
+
18383
630
{\displaystyle {\frac {3}{4}}-{\frac {2}{5}}x+{\frac {9}{4}}x+{\frac {5}{14}}x=-{\frac {1}{2}}+{\frac {6}{7}}x-{\frac {10}{9}}x-1+{\frac {1}{7}}+{\frac {18383}{630}}}
2
3
+
1
14
x
−
3
2
+
1
14
x
+
11
5
−
3
13
−
6
11
x
=
−
9
4
−
1
11
+
29831
8580
{\displaystyle {\frac {2}{3}}+{\frac {1}{14}}x-{\frac {3}{2}}+{\frac {1}{14}}x+{\frac {11}{5}}-{\frac {3}{13}}-{\frac {6}{11}}x=-{\frac {9}{4}}-{\frac {1}{11}}+{\frac {29831}{8580}}}
−
2
x
−
3
5
+
1
3
x
−
4
7
x
+
4
3
x
+
11
7
x
−
7
12
x
=
14
5
x
−
7
13
+
10579
260
{\displaystyle -2x-{\frac {3}{5}}+{\frac {1}{3}}x-{\frac {4}{7}}x+{\frac {4}{3}}x+{\frac {11}{7}}x-{\frac {7}{12}}x={\frac {14}{5}}x-{\frac {7}{13}}+{\frac {10579}{260}}}
−
5
14
x
+
1
2
+
11
13
+
5
8
x
=
−
7
6
−
10
11
x
−
1
14
+
3
2
−
1
3
−
17431
1001
{\displaystyle -{\frac {5}{14}}x+{\frac {1}{2}}+{\frac {11}{13}}+{\frac {5}{8}}x=-{\frac {7}{6}}-{\frac {10}{11}}x-{\frac {1}{14}}+{\frac {3}{2}}-{\frac {1}{3}}-{\frac {17431}{1001}}}
2
3
−
13
14
+
7
4
+
6
7
x
+
6
x
=
−
8
7
+
1
5
−
x
+
5
2
x
−
1229
420
{\displaystyle {\frac {2}{3}}-{\frac {13}{14}}+{\frac {7}{4}}+{\frac {6}{7}}x+6x=-{\frac {8}{7}}+{\frac {1}{5}}-x+{\frac {5}{2}}x-{\frac {1229}{420}}}
14
13
x
−
9
5
x
+
11
2
x
−
2
3
−
1
9
x
=
−
1
5
+
5
x
+
2
3
x
−
1
5
x
+
391
1170
{\displaystyle {\frac {14}{13}}x-{\frac {9}{5}}x+{\frac {11}{2}}x-{\frac {2}{3}}-{\frac {1}{9}}x=-{\frac {1}{5}}+5x+{\frac {2}{3}}x-{\frac {1}{5}}x+{\frac {391}{1170}}}
11
12
x
+
9
10
+
8
9
−
4
5
−
11
+
3
14
x
−
13
5
+
1
7
x
=
−
5
8
−
8609
504
{\displaystyle {\frac {11}{12}}x+{\frac {9}{10}}+{\frac {8}{9}}-{\frac {4}{5}}-11+{\frac {3}{14}}x-{\frac {13}{5}}+{\frac {1}{7}}x=-{\frac {5}{8}}-{\frac {8609}{504}}}
−
9
13
x
+
12
5
x
−
2
3
−
9
4
x
=
−
1
+
1
2
−
10
3
x
+
7
11
x
−
2
x
−
214597
4290
{\displaystyle -{\frac {9}{13}}x+{\frac {12}{5}}x-{\frac {2}{3}}-{\frac {9}{4}}x=-1+{\frac {1}{2}}-{\frac {10}{3}}x+{\frac {7}{11}}x-2x-{\frac {214597}{4290}}}
9
10
x
−
1
7
+
x
−
12
11
−
3
5
=
3
4
x
+
2
7
x
+
1
3
+
7
5
−
68389
4620
{\displaystyle {\frac {9}{10}}x-{\frac {1}{7}}+x-{\frac {12}{11}}-{\frac {3}{5}}={\frac {3}{4}}x+{\frac {2}{7}}x+{\frac {1}{3}}+{\frac {7}{5}}-{\frac {68389}{4620}}}
2
x
−
11
7
+
1
3
x
+
x
−
3
2
x
−
12
11
=
8
13
−
3
11
+
5
9
x
+
107017
18018
{\displaystyle 2x-{\frac {11}{7}}+{\frac {1}{3}}x+x-{\frac {3}{2}}x-{\frac {12}{11}}={\frac {8}{13}}-{\frac {3}{11}}+{\frac {5}{9}}x+{\frac {107017}{18018}}}
1
10
+
8
9
x
−
12
11
x
+
5
6
x
−
7
x
−
2
9
x
+
3
4
=
−
5
11
+
8
5
x
+
2089
220
{\displaystyle {\frac {1}{10}}+{\frac {8}{9}}x-{\frac {12}{11}}x+{\frac {5}{6}}x-7x-{\frac {2}{9}}x+{\frac {3}{4}}=-{\frac {5}{11}}+{\frac {8}{5}}x+{\frac {2089}{220}}}
12
11
+
2
7
+
1
8
x
+
11
14
+
x
−
5
3
+
5
7
−
3
5
=
1
6
−
50951
2310
{\displaystyle {\frac {12}{11}}+{\frac {2}{7}}+{\frac {1}{8}}x+{\frac {11}{14}}+x-{\frac {5}{3}}+{\frac {5}{7}}-{\frac {3}{5}}={\frac {1}{6}}-{\frac {50951}{2310}}}
−
10
13
x
−
11
13
x
−
7
13
−
14
=
−
5
4
x
+
14
5
x
−
7
x
+
x
−
1
6
x
−
37091
780
{\displaystyle -{\frac {10}{13}}x-{\frac {11}{13}}x-{\frac {7}{13}}-14=-{\frac {5}{4}}x+{\frac {14}{5}}x-7x+x-{\frac {1}{6}}x-{\frac {37091}{780}}}
−
13
14
+
6
5
x
+
2
x
+
11
4
x
+
7
=
−
13
8
x
+
7
8
x
+
7
2
+
1
5
+
1959
35
{\displaystyle -{\frac {13}{14}}+{\frac {6}{5}}x+2x+{\frac {11}{4}}x+7=-{\frac {13}{8}}x+{\frac {7}{8}}x+{\frac {7}{2}}+{\frac {1}{5}}+{\frac {1959}{35}}}
−
13
6
x
−
10
3
+
11
2
−
3
8
−
1
=
−
9
−
9
7
x
+
3
2
−
x
+
1373
168
{\displaystyle -{\frac {13}{6}}x-{\frac {10}{3}}+{\frac {11}{2}}-{\frac {3}{8}}-1=-9-{\frac {9}{7}}x+{\frac {3}{2}}-x+{\frac {1373}{168}}}
11
7
+
1
14
−
9
x
−
7
13
−
x
−
7
x
+
12
13
x
−
5
6
x
=
−
1
5
x
+
185491
2730
{\displaystyle {\frac {11}{7}}+{\frac {1}{14}}-9x-{\frac {7}{13}}-x-7x+{\frac {12}{13}}x-{\frac {5}{6}}x=-{\frac {1}{5}}x+{\frac {185491}{2730}}}
תשובות סופיות
עריכה
18
{\displaystyle 18}
3
{\displaystyle 3}
−
12
{\displaystyle -12}
9
{\displaystyle 9}
−
14
{\displaystyle -14}
3
{\displaystyle 3}
−
5
{\displaystyle -5}
−
5
{\displaystyle -5}
−
13
{\displaystyle -13}
9
{\displaystyle 9}
−
21
{\displaystyle -21}
18
{\displaystyle 18}
−
4
{\displaystyle -4}
19
{\displaystyle 19}
15
{\displaystyle 15}
−
2
{\displaystyle -2}
−
18
{\displaystyle -18}
−
13
{\displaystyle -13}
−
1
{\displaystyle -1}
16
{\displaystyle 16}
−
2
{\displaystyle -2}
20
{\displaystyle 20}
−
9
{\displaystyle -9}
9
{\displaystyle 9}
−
6
{\displaystyle -6}
20
{\displaystyle 20}
−
10
{\displaystyle -10}
3
{\displaystyle 3}
−
4
{\displaystyle -4}
0
{\displaystyle 0}
12
{\displaystyle 12}
3
{\displaystyle 3}
−
16
{\displaystyle -16}
−
8
{\displaystyle -8}
11
{\displaystyle 11}
0
{\displaystyle 0}
−
15
{\displaystyle -15}
−
16
{\displaystyle -16}
−
1
{\displaystyle -1}
−
1
{\displaystyle -1}
−
4
{\displaystyle -4}
−
12
{\displaystyle -12}
−
13
{\displaystyle -13}
7
{\displaystyle 7}
−
1
{\displaystyle -1}
−
20
{\displaystyle -20}
−
11
{\displaystyle -11}
8
{\displaystyle 8}
−
1
{\displaystyle -1}
−
4
{\displaystyle -4}
